The Abstraction and Reasoning Corpus: D. Deferred Proofs
by EScholar: Electronic Academic Papers for ScholarsMarch 11th, 2024
Too Long; Didn't Read
State-of-the-art machine learning models struggle with generalization which can only be achieved by proper accounting for core knowledge priors.
This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Mattia Atzeni, EPFL, Switzerland and [email protected];
(2) Mrinmaya Sachan, ETH Zurich, Switzerland;
(3) Andreas Loukas, Prescient Design, Switzerland.
Table of Links
- Abstract & Introduction
- Formalizing the Group-Action Learning Problem
- Attention Masks for Core Geometry Priors
- The LATFORMER Architecture
- Experiments
- Related Work
- Conclusion & References
- A. Additional Details on the Model
- B. Additional Experiments and Details on the Experimental Setup
- C. Limitations and Future Work
- D. Deferred Proofs
D. Deferred Proofs
We prove both Theorem 3.1 and 3.2 by induction on the dimensionality of the hypercubic lattice m.
D.1. Base Case for Theorems 1 and 2
D.2. Inductive Step for Theorems 1 and 2
D.3. Proof of Corollary 1
The proof of Corollary 1 follows immediately from Theorem 3.2 and from the property of the Fourier transform according to which multiplying in the Fourier domain implements a convolution in the original domain.
L O A D I N G
. . . comments & more!
. . . comments & more!
